In a digital video broadcasting-satellite 2 (DVB-S2) standard for a broadband satellite communication broadcast convergence service suitable for a Ka band, bits-to-symbol mapping for 4+12+16 APSK modulation is as shown in FIG. 1.
In the bits-to-symbol mapping, mapping regions for each bit (bh, h=1, 2, . . . , 5) are shown in FIGS. 2A to 2E. At this time the left-most bit is a first bit (b1), that is, a most significant bit (MSB).
The above-mentioned related art has several problems. Since the 4+12+16 APSK modulation of the DVB-S2 is impossible to perform a gray bits-to-symbol mapping, the bit error probability performance may be varied according to the bits-to-symbol mapping algorithm and since signal constellation is formed of three different amplitudes, the bit error performance is changed due to an effect on non-linearity of the high power amplifier.
As can be appreciated from FIGS. 2A to 2E, the bits-to-symbol mapping proposed in the existing standards applies a decision region-based bits-to-symbol algorithm to each bit. However, the bits-to-symbol mapping type of each bit is not symmetrical to I/Q axes and a Hamming distance between adjacent symbols is up to 3 as can be appreciated from FIG. 1. As shown in FIG. 3, when a set of signal constellations on an inner circle is sI={s4, s12, s20, s28}, a set of signal constellations on an intermediate circle is sM={s2, s5, s8, . . . , s32}, and a set of signal constellations on an outer circle is sO={s1, s3, s6, . . . , s31}, the maximum Hamming distance according to the standard bits-to-symbol algorithm shown in FIG. 1 depends on the following Equation 1.H—d(s5,s6)=H—d(s21,s22)=3  [Equation 1]
Since the bit error probability is inversely proportional to the Hamming distance between adjacent symbols, the Hamming distance of 3 is a direct factor of the error performance deterioration. FIG. 3 shows the signal constellations according to the 4+12+16 APSK modulation using input backoff of 9 dB and the effect of the non-linear high power amplifier (HPA), and the change in the signal constellation and the decision boundary accordingly. When there is non-linearity due to the AM/AM and AM/PM distortions of the high power amplifier, it can be appreciated from FIG. 3 that the positions of the signal constellations are changed. In other words, it can be appreciated that the signal constellations of the intermediate circle approaches the signal constellations of the outer circle. This means that a Euclidean distance is short and the shortened Euclidean distance causes the degradation of the error performance. In particular, reviewing the Euclidean distance of the signal constellations having the above-mentioned Hamming distance at maximum of 3, it can be appreciated that the Euclidean distance thereof is closest. This is a main factor of the deterioration of the entire bit error performance.